The objective of this bulletin is to provide detailed guidance for sizing rupture discs using standard methodologies found in ASME Section VIII Div. 1, API RP520, and Crane TP-410. To assist in the sizing process, **Fike offers DisCalc™**, a web based sizing program.

## Overpressure Allowance

When sizing pressure relief devices, the ASME Code defines the maximum pressure that may build up in the pressure vessel while the device is relieving. This pressure varies depending on the application of the device. The following table defines the various overpressure allowances. See technical bulletin TB8100 for ASME application requirements.

## Rupture Disc Sizing Methodologies

Three basic methodologies for sizing rupture disc devices are described below. These methods assume single phase, non-reactive fluid flow. Resources such as API RP520 Part 1, the DIERS Project Manual, and CCPS Guidelines for Pressure Relief and Effluent Handling Systems provide other methods for two-phase, flashing, reactive, and otherwise non-steady state conditions.

##### Coefficient of discharge method (K_{D})

The K_{D} is the coefficient of discharge that is applied to the theoretical flow rate to arrive at a rated flow rate for simple systems.

##### Resistant to flow method (K_{R})

The K_{R} represents the velocity head loss due to the rupture disc device. This head loss is included in the overall system loss calculations to determine the size of the relief system.

##### Combination capacity method

When a rupture disc device is installed in combination with a pressure relief valve (PRV), the valve capacity is de-rated by a default value of 0.9 or a tested value for the disc/valve combination. See **technical bulletin TB8105** for specific application requirements when using rupture disc devices in combination with PRVs. A listing of Fike certified combination factors can be found in **technical bulletin TB8103**.

## Coefficient of Discharge Method (K_{D})

Use this method for simple systems where the following conditions are true (8 & 5 Rule). This method takes into account the vessel entrance effects, 8 pipe diameters of inlet piping, 5 pipe diameters of discharge piping, and effects of discharging to atmosphere.

## Gas/Vapor Sizing

Determination of Critical vs. Subcritical Flow per API RP520

Critical Pressure:

### Calculations per ASME Section VIII (assumes critical flow)

Critical Flow:

### Calculation per API RP520

Subcritical Flow:

Critical Flow:

TABLE 1

Gas Constants

TABLE 2

Gas Flow Constant C for Sonic Flow STEAM SIZING

## Steam Sizing

### Calculation per ASME Section VIII

Steam:

### Calculation per API RP520

Steam:

TABLE 3

Superheat Correction Factors, K_{SH} (API RP520 Part 1 Table 9)

## Liquid Sizing

### Calculation per ASME Section VIII

Water:

### Calculation per API RP520

Non-viscous liquid:

Viscous Liquid:

For viscous liquid sizing, first calculate A_{R} using K_{V} of 1.0.

Apply the area A of the next larger size disc to the Reynolds number calculations to arrive at K_{V}. Then re-calculate required area A_{V} using the derived K_{V}.

## Resistance to Flow Method (K_{R})

Use this method when the 8 & 5 Rule does not apply and the rupture disc is not installed in combination with a pressure relief valve. This type of calculation is the responsibility of the system designer. (DisCalc^{TM} does not perform this type of calculation.)

### Characteristics of the Resistance to Flow Method

• Sizing is done on a relief system basis not by capacity of individual components

• Rupture disc is treated as another component in the relief system

• Each device or family of devices has a unit-less resistance value (K_{R}) that represents the expected resistance to flow that is independent of the fluid flowing

• System relief capacity must be multiplied by a factor of 0.90

### Types of K_{R}

Because many rupture discs have different opening characteristics depending on whether they are opened with a compressed vapor or incompressible liquid, there are certified KR values that are denoted by the applicable service media. The K_{R} values for different media are a result of differences in how the rupture disc opens with different media and test methods that have been standardized in ASME PTC25. A list of Fike certified K_{R} factors can be found in technical bulletin TB8104.

• Air or gas service – K_{RG}

Use K_{RG} when the media is a gas or vapor, or when the media is liquid but there is a significant vapor volume directly in contact with the disc at the time of rupture

• Liquid service – K_{RL}

Use KRL when the media is liquid and the liquid is against the disc at the time of rupture

• Air or gas and liquid service – K_{RGL}

K_{RGL} can be used for any service conditions

The following examples will illustrate how K_{R} values are used to establish the flow capacity of a pressure relief piping system.

## Vapor Sizing

The following example, see Figure 1, assumes that k = cp/cv = 1.4 which results in a conservative calculation. The example shown is based on Crane TP-410 methods. It also assumes a steady state relieving condition where the vessel volume is large relative to the relieving capacity.

Given information:

- Pressure vessel MAWP = 1000 psig
- Relieving pressure as allowed by ASME Section VIII Div. 1 = 110% x MAWP = 1114.7 psia = P’1
- Back pressure (outlet pressure) = 14.7 psia
- Working fluid – air (k = c /c = 1.4)
- Air temperature at disc rupture = 500°F = 960R = T
- Maximum flow rate into the vessel = 20,000 SCFM
- Rupture Disc – Fike 3” SRX-GI g K = 0.99

### Determine the Total Piping System Resistance Factor:

The Darcy Equation defines the discharge of compressible fluids through valves, fittings and pipes. Since the flow rate into the example vessel is defined in SCFM, the following form of the Darcy equation is used:

Crane Equation 3-20

To determine Y, first it must be determined if the flow will be sonic or subsonic. This is determined by comparing the actual DP/P’_{1} to the limiting DP/P’_{1} for sonic flow. Crane Table A-22 shows limiting factors for k=1.4 for sonic flow at the known value of K_{T}.

If (DP/P’_{1})_{sonic} < (DP/P’_{1})_{actual}, then the flow will be sonic.

Limiting Factors for Sonic Velocity (k=1.4) Excerpt from Crane 410, Pg A-22

For this example:

From table A-22 at KT=7.33

Since (DP/P’1)_{sonic} = 0.754, then DP = 0.754 * P’_{1} = 0.754 * 1114.7 = 840.5 psig

Calculating the system capacity is completed by substituting the known values into Crane 410 Equation 3-20.

The ASME Pressure Vessel Code, Section VIII, Division 1, paragraph UG-127(a)(2), also requires that the calculated system capacity using the resistance to flow method must also be multiplied by a factor of 0.90 or less to account for uncertainties inherent with this method.

Thus, the system capacity is greater than the required process capacity (20,000 SCFM)

### Liquid Sizing

For this example Figure 2 is assumed, water will be considered the flow media. The example shown is based on Crane TP-410 methods. It also assumes a steady state relieving condition where the vessel volume is large relative to the relieving capacity.

Given information:

• Pressure vessel MAWP = 500 psig

• Relieving pressure as allowed by

ASME Section VIII Div. 1 = 110% x MAWP = 550 psig = P1

• Back pressure (outlet pressure) = 1 psig = P2

• Working fluid – water

• Temperature = 70°F

• Maximum flow rate into the vessel = 50 ft3/min

• Rupture disc – Fike 2” SRL-GI → K_{RGL }= 0.59

From Crane 410:

“Bernoulli’s Theorem is a means of expressing the application of the law of conservation of energy to the flow of fluids in a conduit (piping). The total energy at any particular point, above some arbitrary horizontal datum plane, is equal to the sum of the elevation head (Z), the pressure head (P), the velocity head (V).

In real applications, there are energy losses in piping systems between states (or location) 1 and 2. Those losses are accounted for in the term hL, which are predominately frictional head losses. The energy balance is then expressed:

** **

Crane Equation 1-3

As in the previous example, head losses due to friction in the piping and the head losses due to fittings are proportional to the sum of the flow resistances:

Since the actual head loss is velocity dependent,

Frictional loss coefficients and fitting loss coefficients for the example are as follows:

Thus,

Other known conditions:

V_{vessel} = 0 ft/sec

Z_{vessel} = 0 ft

Z_{vessel} = 1 ft + 20 ft = 21 ft = elevation change of piping

P_{exit} = 0 ft/sec

ρ1 = ρ2 = 62.3 lb/ft^{3} for water at room temperature

Substituting values into Equation 1-3,

Solving for V_{2} (exit velocity),

V_{2} = 89.82 ft/sec

The friction factor used earlier in the calculations for piping frictional losses assumed that the flow in the pipes was fully turbulent flow. The value of the friction factor is related to the Reynolds Number (Re) of the resulting flow (Ref: Crane 410 pg 1-1). For Re< 2000, the flow is laminar and the friction factor is a function of Reynolds Number, only. For Re >4000, the flow is fully turbulent and the friction factor is also a function of the character of the piping wall (relative roughness).

The friction factor used earlier must be verified. First calculate the Reynolds Number:

** **

Since the Reynolds Number is >4000, the flow is turbulent, and the friction factor is now a function of the relative roughness of the pipe. From Crane 410 Figure A-23, the friction factor, f, for 2” commercial steel pipe in fully turbulent flow is 0.019. This verifies the original assumption for friction factor.

Now that the fluid velocity is known, the volumetric flow rate can be calculated.

Q = A ×V

Where:

Q = volumetric flow rate (ft^{3}/sec)

A = area of pipe (ft^{2}) – pd2/4

V = fluid velocity (ft/sec)

Substituting values,

Per the ASME Code, the rated system capacity is,

Q_{rated} = Q_{calc} × (0.90) = 125.6 × (0.90) = 113.04 ft^{3}/min

Therefore, the relief system can flow the required 50 ft^{3}/min.

##### References:

^{American Society of Mechanical Engineers, Boiler and Pressure Vessel Code Section VIII, Division 1 American Society of Mechanical Engineers, PTC25}

^{American Petroleum Institute, RP520 Crane Valves, Technical Paper 410}

^{Crane Valves, Crane Companion Computer Program}

^{Fike Technical Bulletin TB8100 ASME Code and Rupture Discs}

^{Fike Technical Bulletin TB8103 Certified Combination Capacity Factors }

^{Fike Technical Bulletin TB8104 Certified KR and MNFA Values}

^{Fike Technical Bulletin TB8105 Best Practices for RD & PRV Combinations}

^{DIERS Project Manual}

^{CCPS Guidelines for Pressure Relief Effluent Handling Systems}